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When many individual plaintiffs have similar claims against the same defendant, often it is more efficient for them to be combined into a single class action. Due to their increased complexity and larger stakes, in the USA there are special criteria a party seeking to proceed as a class action needs to satisfy. Statistical evidence is often submitted to establish that the members of the proposed class were affected by a common event or policy. In equal employment cases involving an employer with a number of locations or subunits, defendants may argue that the data should be examined separately for each unit, while plaintiffs may pool the data into one or several large samples or focus on a few units in which statistical significance was observed. After describing the statistical issues involved, it will be seen that requiring plaintiffs to demonstrate a statistically significant disparity in a pre-set fraction, e.g. majority of the subunits is too stringent as the power of the statistical test to detect a meaningful disparity in most subunits is too small. On the other hand, when many statistical tests are calculated on data from a fair system, a small percentage of significant disparities will be obtained. Thus, allowing a class action to proceed if the plaintiffs can demonstrate a statistically significant difference in a few subunits is too lax. The use of established methods for combining statistical tests for data organized by appropriate subgroups will be illustrated on data from two recent cases. Using the concept of power, the expected number,  E , of subunits in which a statistically significant result would occur if there were a legally meaningful disparity can be determined. Then the observed number,  O , of units with a significant disparity can be compared to  E , to see whether data are consistent with a pattern,  O  close to  E , indicating unfairness or  O  clearly less than  E , reflecting fairness. Without such a comparison, the number of units with a statistically significant disparity is not meaningful. Both parties in  Dukes  v.  Wal-mart  introduced summaries of the  p -values of many individual statistical tests that grouped them into a small number of categories. An appropriate overall procedure combines them into a single summary statistic. This analysis shows that the promotion data for the 40 or 41 regions in the Wal-mart case are consistent with an overall system in which the odds an eligible female being promoted were about 70–80% of those of a male. A similar analysis of the  p -values of Wal-mart's subunit regressions also is consistent with a general pattern of a degree of underpayment of female employees relative to that of similarly qualified males.

law, probability and risk

Some important statistical issues courts should consider in their assessment of statistical analyses submitted in class certification motions: implications for  Dukes  v.  Wal-mart